In this paper, we propose a dueling double deep Q-network (DDQN)-based adaptive multi-objective handover framework for low Earth orbit (LEO) satellite networks. The proposed method enables dynamic trade-off learning among throughput, blocking probability, and switching cost under time-varying network conditions. Simulation results demonstrate that the proposed approach consistently outperforms conventional baselines, achieving up to 10.3% throughput improvement and near-zero blocking under typical operating conditions.